Rich people can buy high end homes that they know will appreciate in value, and their interest rate will be lower because they are wealthy. So if they get a good enough rate they are basically getting a tax break for what they are paying for the house and then selling it for more profit. They can do this because they are wealthy enough to decide on when to make large transactions.

As a deduction it will have a far higher impact on their taxes because whatever the amount is paid in interest is coming out of their highest tax bracket.

So if they are paying 10k in interest on a more expensive house becsuse rheir interest rate is lower and the 10k reduced their income taxed at 20+% they will get a far bigger benefit out of it than someone paying 10k at a higher interest rate that might lower their income taxed at 10% and when they sell their house they will get less of an increase from it.